GENERAL THEORY OF RElATIVITY
In 1916 Einstein advanced his theory of relativity greatly by making it apply to observers (reference frames) moving nonuniformly relative to each other. ature's fundamental laws, he reasoned, remain invariant throughout the universe in all frames of reference, whether the observers are accelerated or not.
In his second law of motion Newton had showed that the force it takes to accelerate a body is proportional to its inertial mass. (Inertia is the resistance a body offers to an applied force.) He was also aware that the gravitational force on a body is proportional to its gravitational mass. Otherwise, bodies of different masses would not fall to the ground at the same rate-that is, with constant acceleration-as we know they do. In 1889 a Hungarian physicist, Baron von Eotvos, first proved experimentally and very precisely that inertial mass and gravitational mass are equivalent, an equality that had long been taken for granted. Modern experiments confirm that the inertial mass and the gravitational mass are the same to about one part in 1012 .
Einstein argued that the equality of inertial and gravitational mass must mean that "the same quality of a body manifests itself according to circumstances as inertia' or as 'weight'. The consequence of this is that it is impossible to distinguish between the effect of an inertial force or a gravitational force on accelerated motion. He worked the idea into this principle:
PRINCIPLE OF EQUIVALENCE: A gravitational force can be replaced by an inertial force that is due to accelerated motion without any change in the physical activity.
By way of illustration imagine an observer in a rocket ship constantly accelerating to 1g. Because 1g of acceleration is the acceleration we experience on the surface of the earth, the observer -hould experience within his reference frame defined by the cabin of the rocket ship) what he would experience on the su rface of the earth. To show this, suppose he has some sort of ball in one hand. When the ship is in position 1, he releases the ball. It continues to move upward with the velocity the ship had at the moment of release (the successive positions along the lower broken line(Uaccelerating rocket ship illustration). If the ship were moving upward at constant velocity, the ball would remain suspended in the same place because ship and ball move the same amount. But the ship is accelerating; so the floor moves upward faster than the ball, colliding with the ball in position 4. The observer in the ship could attribute this to the force of gravity of some massive body if he does not know he is accelerating. From a vantage point outside the ship, however, another observer has been watchingwhat is going on inside. The second observer's explanation of the sequence of events is simple; All those actions are explained by the ship's accelerated motion, and one need not postulate a gravitational force.
Einstein pointed out that each observer has a right to his or her own description of events. We can replace the force of gravity by an inertial force caused by an accelerated motion. An inertial force is not a real force but an effect of the nonuniform motion of the observer's frame of reference. You have al ready experienced such a fictitious force from accelerated motion while standing on the floor of a merry-go-round. You felt a force called a centrifugal force, that tended to move you toward the rim.
In general-relativity theory spatial cu rvature of local space-time is dictated by the presence of material bodies. If no mass is there, the curvature of nearby space is zero, and it is a flat space whose geometrical properties are described by ordinary Euclidean geometry (the kind you learned in high school). In the warped geometry of space-time that surrounds a large mass less massive objects move along curved paths. A planet's elliptical motion is an example: The planet moves in a curved path in the warped space surrounding the sun. The only way we have of illustrating curved space for you is in two dimensions rather than three.
The force we call "gravity," then, is nothing more than natural behavior by bodies moving within the geometrical framework of space-time. The Newtonian would say that the body moves according to action from a distance dictated by a force called gravity. The Einsteinian says that a body moves naturally in response to the local structure of curved space-time.
Massive bodies, in addition to warping space in their vicinities, also alter time. If we could position ourselves where there is little if any warping of spacetime, far from a massive body, and watch what happens as a clock approaches the massive body, we should see the clock ticking slower and slower, the closer it gets. Clearly the realm of space-time in the immediate vicinity of massive bodies is different from that far from any mass.We may summarize motion in general relativity with the following principle:
PRINCIPLE OF GENERAL RELATIVITY: Curved space-time tells matter how to move, and in turn matter tells local space-time how to curve.
